Independent Component Analysis Estimation Research Articles

Identification of Structural VAR Models via Independent Component Analysis: A Performance Evaluation Study

Independent Component Analysis (ICA) is a statistical method that linearly transforms a random vector. Under the assumption that the observed data are mixtures of non-Gaussian and independent processes, ICA is able to recover the underlying components, but with a scale and order indeterminacy. Its application to structural vector autoregressive (SVAR) models allows the researcher to recover the impact of independent structural shocks on the observed series from estimated residuals. We analyze different ICA estimators, recently proposed within the field of SVAR analysis, and compare their performance in recovering structural coefficients. Moreover, we assess the size distortions of the estimators in hypothesis testing. We conduct our analysis by focusing on non-Gaussian distributional scenarios that get gradually close to the Gaussian case. The latter is the case where ICA methods fail to recover the independent components. Although the ICA estimators that we analyze show similar pattern of performance, two of them — the fastICA algorithm and the pseudo-maximum likelihood estimator — tend to perform relatively better in terms of variability, stability across sub- and super-Gaussian settings, and size distortion. We finally present an empirical illustration using US data to identify the effects of government spending and tax cuts on economic activity, thus providing an example where ICA techniques can be used for hypothesis testing.

Multi-spatial-scale dynamic interactions between functional sources reveal sex-specific changes in schizophrenia.

We introduce an extension of independent component analysis (ICA), called multiscale ICA, and design an approach to capture dynamic functional source interactions within and between multiple spatial scales. Multiscale ICA estimates functional sources at multiple spatial scales without imposing direct constraints on the size of functional sources, overcomes the limitation of using fixed anatomical locations, and eliminates the need for model-order selection in ICA analysis. We leveraged this approach to study sex-specific and sex-common connectivity patterns in schizophrenia. Results show dynamic reconfiguration and interaction within and between multi-spatial scales. Sex-specific differences occur (a) within the subcortical domain, (b) between the somatomotor and cerebellum domains, and (c) between the temporal domain and several others, including the subcortical, visual, and default mode domains. Most of the sex-specific differences belong to between-spatial-scale functional interactions and are associated with a dynamic state with strong functional interactions between the visual, somatomotor, and temporal domains and their anticorrelation patterns with the rest of the brain. We observed significant correlations between multi-spatial-scale functional interactions and symptom scores, highlighting the importance of multiscale analyses to identify potential biomarkers for schizophrenia. As such, we recommend such analyses as an important option for future functional connectivity studies.

Compressive independent component analysis: theory and algorithms

Abstract Compressive learning forms the exciting intersection between compressed sensing and statistical learning where one exploits sparsity of the learning model to reduce the memory and/or computational complexity of the algorithms used to solve the learning task. In this paper, we look at the independent component analysis (ICA) model through the compressive learning lens. In particular, we show that solutions to the cumulant-based ICA model have a particular structure that induces a low-dimensional model set that resides in the cumulant tensor space. By showing that a restricted isometry property holds for random cumulants e.g. Gaussian ensembles, we prove the existence of a compressive ICA scheme. Thereafter, we propose two algorithms of the form of an iterative projection gradient and an alternating steepest descent algorithm for compressive ICA, where the order of compression asserted from the restricted isometry property is realized through empirical results. We provide analysis of the CICA algorithms including the effects of finite samples. The effects of compression are characterized by a trade-off between the sketch size and the statistical efficiency of the ICA estimates. By considering synthetic and real datasets, we show the substantial memory gains achieved over well-known ICA algorithms by using one of the proposed CICA algorithms.

Identification of Structural VAR Models Via Independent Component Analysis: A Performance Evaluation Study

Independent Component Analysis (ICA) is a statistical method that transforms a set of random variables in least dependent linear combinations. Under the assumption that the observed data are mixtures of non-Gaussian and independent processes, ICA is able to recover the underlying components, but a scale and order indeterminacy. Its application to structural vector autoregressive (SVAR) models allows the researcher to recover the impact of independent structural shocks on the observed series from estimated residuals. We analyze different ICA estimators, recently proposed within the field of SVAR identification, and compare their performance in recovering structural coefficients. Moreover, after suggesting an algorithm that solve the ICA indeterminacy problem, we assess the size distortions of the estimators in hypothesis testing. We conduct our analysis by focusing on distributional scenarios that get gradually close the Gaussian case, which is the case where ICA methods fail to recover the independent components. In terms of statistical properties of the ICA estimators, we find no evidence that a method outperforms all others. We finally present an empirical illustration using US data to identify the effects of government spending and tax cuts on economic activity, thus providing an example where ICA techniques can be used for hypothesis testing.

Efficient Estimation of the Helicopter Blade Parameter by Independent Component Analysis

We propose an efficient method to estimate various parameters of a helicopter blade including the number B num and the length by separating the blade signal using independent component analysis (ICA) and an analytic solution obtained by monostatic/bistatic geometry. The proposed method is composed of two parts, one for even B num and one for odd B num . For even B num the blade parameters are estimated using ICA plus analytic estimation. For odd B num the parameters are estimated using two ICAs plus analytic estimation. Experimental results using the radar signal of a blade model calculated by physical optics demonstrate that the proposed method successfully separates the blade signals for both even and odd B num s and estimates parameters with high accuracy.

Application of ICA to realistically simulated (1)H-MRS data.

Introduction1H-MRS signals from brain tissues capture information on in vivo brain metabolism and neuronal biomarkers. This study aims to advance the use of independent component analysis (ICA) for spectroscopy data by objectively comparing the performance of ICA and LCModel in analyzing realistic data that mimics many of the known properties of in vivo data.MethodsThis work identifies key features of in vivo 1H-MRS signals and presents methods to simulate realistic data, using a basis set of 12 metabolites typically found in the human brain. The realistic simulations provide a much needed ground truth to evaluate performances of various MRS analysis methods. ICA is applied to collectively analyze multiple realistic spectra and independent components identified with our generative model to obtain ICA estimates. These same data are also analyzed using LCModel and the comparisons between the ground-truth and the analysis estimates are presented. The study also investigates the potential impact of modeling inaccuracies by incorporating two sets of model resonances in simulations.ResultsThe simulated fid signals incorporating line broadening, noise, and residual water signal closely resemble the in vivo signals. Simulation analyses show that the resolution performances of both LCModel and ICA are not consistent across metabolites and that while ICA resolution can be improved for certain resonances, ICA is as effective as, or better than, LCModel in resolving most model resonances.ConclusionThe results show that ICA can be an effective tool in comparing multiple spectra and complements existing approaches for providing quantified estimates.

Cramér-Rao Bound for Circular and Noncircular Complex Independent Component Analysis

Despite an increased interest in complex independent component analysis (ICA) during the last two decades, a closed form expression for the Cramér-Rao bound (CRB) for the demixing matrix is not known yet. In this paper, we fill this gap by deriving a closed-form expression for the CRB of the demixing matrix for instantaneous noncircular complex ICA. It contains the CRB for circular complex ICA and noncircular complex Gaussian ICA as two special cases. We also study the CRB numerically for the family of noncircular complex generalized Gaussian distributions and compare it to simulation results of two ICA estimators. Furthermore, we show how to extend the CRB to the case where the source signals are not temporally independent and identically distributed.

An independent component analysis filtering approach for estimating continental hydrology in the GRACE gravity data

An approach based on Independent Component Analysis (ICA) has been applied on a combination of monthly GRACE satellite solutions computed from official providers (CSR, JPL and GFZ), to separate useful geophysical signals from important striping undulations. We pre-filtered the raw GRACE Level-2 solutions using Gaussian filters of 300, 400, 500-km of radius to verify the non-Gaussianity condition which is necessary to apply the ICA. This linear inverse approach ensures to separate components of the observed gravity field which are statistically independent. The most energetic component found by ICA corresponds mainly to the contribution of continental water mass change. Series of ICA-estimated global maps of continental water storage have been produced over 08/2002–07/2009. Our ICA estimates were compared with the solutions obtained using other post-processing of GRACE Level-2 data, such as destriping and Gaussian filtering, at global and basin scales. Besides, they have been validated with in situ measurements in the Murray–Darling Basin. Our computed ICA grids are consistent with the different approaches. Moreover, the ICA-derived time series of water masses showed less north–south spurious gravity signals and improved filtering of unrealistic hydrological features at the basin-scale compared with solutions obtained using other filtering methods.

Compact CramÉr–Rao Bound Expression for Independent Component Analysis

Despite of the increased interest in independent component analysis (ICA) during the past two decades, a simple closed form expression of the Cramer-Rao bound (CRB) for the demixing matrix estimation has not been established in the open literature. In the present paper we fill this gap by deriving a simple closed-form expression for the CRB of the demixing matrix directly from its definition. A simulation study comparing ICA estimators with the CRB is given.

A feature-selective independent component analysis method for functional MRI.

In this work, we propose a simple and effective scheme to incorporate prior knowledge about the sources of interest (SOIs) in independent component analysis (ICA) and apply the method to estimate brain activations from functional magnetic resonance imaging (fMRI) data. We name the proposed method as feature-selective ICA since it incorporates the features in the sample space of the independent components during ICA estimation. The feature-selective scheme is achieved through a filtering operation in the source sample space followed by a projection onto the demixing vector space by a least squares projection in an iterative ICA process. We perform ICA estimation of artificial activations superimposed into a resting state fMRI dataset to show that the feature-selective scheme improves the detection of injected activation from the independent component estimated by ICA. We also compare the task-related sources estimated from true fMRI data by a feature-selective ICA algorithm versus an ICA algorithm and show evidence that the feature-selective scheme helps improve the estimation of the sources in both spatial activation patterns and the time courses.

Input variable selection: mutual information and linear mixing measures

Determining the most appropriate inputs to a model has a significant impact on the performance of the model and associated algorithms for classification, prediction, and data analysis. Previously, we proposed an algorithm ICAIVS which utilizes independent component analysis (ICA) as a preprocessing stage to overcome issues of dependencies between inputs, before the data being passed through to an input variable selection (IVS) stage. While we demonstrated previously with artificial data that ICA can prevent an overestimation of necessary input variables, we show here that mixing between input variables is common in real-world data sets so that ICA preprocessing is useful in practice. This experimental test is based on new measures introduced in this paper. Furthermore, we extend the implementation of our variable selection scheme to a statistical dependency test based on mutual information and test several algorithms on Gaussian and sub-Gaussian signals. Specifically, we propose a novel method of quantifying linear dependencies using ICA estimates of mixing matrices with a new linear mixing measure (LMM).

Independent component analysis of fMRI group studies by self-organizing clustering

Independent component analysis (ICA) is a valuable technique for the multivariate data-driven analysis of functional magnetic resonance imaging (fMRI) data sets. Applications of ICA have been developed mainly for single subject studies, although different solutions for group studies have been proposed. These approaches combine data sets from multiple subjects into a single aggregate data set before ICA estimation and, thus, require some additional assumptions about the separability across subjects of group independent components. Here, we exploit the application of similarity measures and a related visual tool to study the natural self-organizing clustering of many independent components from multiple individual data sets in the subject space. Our proposed framework flexibly enables multiple criteria for the generation of group independent components and their random-effects evaluation. We present real visual activation fMRI data from two experiments, with different spatiotemporal structures, and demonstrate the validity of this framework for a blind extraction and selection of meaningful activity and functional connectivity group patterns. Our approach is either alternative or complementary to the group ICA of aggregated data sets in that it exploits commonalities across multiple subject-specific patterns, while addressing as much as possible of the intersubject variability of the measured responses. This property is particularly of interest for a blind group and subgroup pattern extraction and selection.

Does independent component analysis play a role in unmixing hyperspectral data?

Independent component analysis (ICA) has recently been proposed as a tool to unmix hyperspectral data. ICA is founded on two assumptions: 1) the observed spectrum vector is a linear mixture of the constituent spectra (endmember spectra) weighted by the correspondent abundance fractions (sources); 2)sources are statistically independent. Independent factor analysis (IFA) extends ICA to linear mixtures of independent sources immersed in noise. Concerning hyperspectral data, the first assumption is valid whenever the multiple scattering among the distinct constituent substances (endmembers) is negligible, and the surface is partitioned according to the fractional abundances. The second assumption, however, is violated, since the sum of abundance fractions associated to each pixel is constant due to physical constraints in the data acquisition process. Thus, sources cannot be statistically independent, this compromising the performance of ICA/IFA algorithms in hyperspectral unmixing. This paper studies the impact of hyperspectral source statistical dependence on ICA and IFA performances. We conclude that the accuracy of these methods tends to improve with the increase of the signature variability, of the number of endmembers, and of the signal-to-noise ratio. In any case, there are always endmembers incorrectly unmixed. We arrive to this conclusion by minimizing the mutual information of simulated and real hyperspectral mixtures. The computation of mutual information is based on fitting mixtures of Gaussians to the observed data. A method to sort ICA and IFA estimates in terms of the likelihood of being correctly unmixed is proposed.

Independent component analysis of fMRI data in the complex domain

In BOLD fMRI a series of MR images is acquired and examined for task-related amplitude changes. These functional changes are small, so it is important to maximize detection efficiency. Virtually all fMRI processing strategies utilize magnitude information and ignore the phase, resulting in an unnecessary loss of efficiency. As the optimum way to model the phase information is not clear, a flexible modeling technique is useful. To analyze complex data sets, independent component analysis (ICA), a data-driven approach, is proposed. In ICA, the data are modeled as spatially independent components multiplied by their respective time-courses. There are thus three possible approaches: 1) the time-courses can be complex-valued, 2) the images can be complex-valued, or 3) both the time-courses and the images can be complex-valued. These analytic approaches are applied to data from a visual stimulation paradigm, and results from three complex analysis models are presented and compared with magnitude-only results. Using the criterion of the number of contiguous activated voxels at a given threshold, an average of 12-23% more voxels are detected by complex-valued ICA estimation at a threshold of /Z/ > 2.5. Additionally, preliminary results from the complex models reveal a phase modulation similar to the magnitude time-course in some voxels, and oppositely modulated in other voxels.